Lithographic Focus and Dose Measurement Using A 2-D Target

ABSTRACT

In order to determine whether an exposure apparatus is outputting the correct dose of radiation and its projection system is focusing the radiation correctly, a test pattern is used on a mask for printing a specific marker onto a substrate. This marker is then measured by an inspection apparatus, such as a scatterometer, to determine whether there are errors in focus and dose and other related properties. The test pattern is configured such that changes in focus and dose may be easily determined by measuring the properties of a pattern that is exposed using the mask. The test pattern may be a 2D pattern where physical or geometric properties, e.g., pitch, are different in each of the two dimensions. The test pattern may also be a one-dimensional pattern made up of an array of structures in one dimension, the structures being made up of at least one substructure, the substructures reacting differently to focus and dose and giving rise to an exposed pattern from which focus and dose may be determined.

This application incorporates by reference in their entireties U.S.patent application Ser. No. 13/062,861, filed Jun. 13, 2011 and U.S.provisional application 61/103,078, filed Oct. 6, 2008.

FIELD OF THE INVENTION

The present invention relates to methods of inspection usable, forexample, in the manufacture of devices by lithographic techniques.Specifically, the present invention relates to a pattern for printing amarker on a substrate for testing focus and dose related properties of alithographic apparatus. The invention relates also to the maskcontaining the pattern, to the substrate containing the marker, to theexposure apparatus that prints the marker, to the inspection apparatusthat tests the marker and to the methods involved.

RELATED ART

A lithographic apparatus is a machine that applies a desired patternonto a substrate, usually onto a target portion of the substrate. Alithographic apparatus can be used, for example, in the manufacture ofintegrated circuits (ICs). In that instance, a patterning device, whichis alternatively referred to as a mask or a reticle, may be used togenerate a circuit pattern to be formed on an individual layer of theIC. This pattern can be transferred onto a target portion (e.g.,comprising part of, one, or several dies) on a substrate (e.g., asilicon wafer). Transfer of the pattern is typically via imaging onto alayer of radiation-sensitive material (resist) provided on thesubstrate. In general, a single substrate will contain a network ofadjacent target portions that are successively patterned. Knownlithographic apparatus include so-called steppers, in which each targetportion is irradiated by exposing an entire pattern onto the targetportion at one time, and so-called scanners, in which each targetportion is irradiated by scanning the pattern through a radiation beamin a given direction (the “scanning” direction) while synchronouslyscanning the substrate parallel or anti-parallel to this direction. Itis also possible to transfer the pattern from the patterning device tothe substrate by imprinting the pattern onto the substrate.

In order to monitor the lithographic process, it is necessary to measureparameters of the patterned substrate, for example the overlay errorbetween successive layers formed in or on it. There are varioustechniques for making measurements of the microscopic structures formedin lithographic processes, including the use of scanning electronmicroscopes and various specialized tools. One form of specializedinspection tool is a scatterometer in which a beam of radiation isdirected onto a target on the surface of the substrate and properties ofthe scattered or reflected beam are measured. By comparing theproperties of the beam before and after it has been reflected orscattered by the substrate, the properties of the substrate can bedetermined. This can be done, for example, by comparing the reflectedbeam with data stored in a library of known measurements associated withknown substrate properties. Two main types of scatterometer are known.Spectroscopic scatterometers direct a broadband radiation beam onto thesubstrate and measure the spectrum (e.g., intensity as a function ofwavelength) of the radiation scattered into a particular narrow angularrange. Angularly resolved scatterometers use a monochromatic radiationbeam and measure the intensity of the scattered radiation as a functionof angle.

Scatterometers may be used to measure several different aspects oflithographic apparatuses, including their substrate orientation andexposure efficacy. Two important parameters of a lithographic apparatusand specifically of the exposure action that the lithographic apparatuscarries out that may also be measured by scatterometers are focus anddose. Specifically, a lithographic apparatus has a radiation source anda projection system as mentioned below. The dose of radiation that isprojected onto a substrate in order to expose it is controlled byvarious parts of the exposure or lithographic apparatus. It is mostlythe projection system of the lithographic apparatus that is responsiblefor the focus of the radiation onto the correct portions of thesubstrate. It is important that the focusing occurs at the level of thesubstrate, rather than before or afterwards so that the sharpest imagewill occur at the level of the substrate and the sharpest patternpossible may be exposed thereon. This enables smaller product patternsto be printed.

The focus and dose of the radiation directly affect the parameters ofthe patterns or structures that are exposed on the substrate. Parametersthat can be measured using a scatterometer are physical properties ofstructures that have been printed onto a substrate such as the criticaldimension (CD) or sidewall angle (SWA) of, for example, a bar-shapedstructure. The critical dimension is effectively the mean width of astructure, for example, such as a bar, space, dot or hole, depending onthe measured structures. The sidewall angle is the angle between thesurface of the substrate and the rising or falling, portion of thestructure.

In addition, mask shape corrections, for example, such as focuscorrections for correcting for the bending of a mask, can be applied ifscribe lane structures are used with a product mask for focusmeasurements.

Focus and dose have been determined simultaneously by scatterometry, orscanning electron microscopy, from one-dimensional structures in themask pattern, which gives rise to one-dimensional markers on thesubstrate, from which measurements are taken. A single structure can beused as long as that structure, when exposed and processed, has a uniquecombination of critical dimension and sidewall angle measurements foreach point in a focus energy matrix (FEM). If these unique combinationsof critical dimension and sidewall angle are available, the focus anddose values can be uniquely determined from these measurements.

However, there is a problem with this use of one-dimensional structures.There are generally a plurality of combinations of focus and dose thatresult in similar critical dimension and sidewall angle measurements.This means that focus and dose cannot be determined uniquely bymeasuring a single one-dimensional structure. It has been considered touse more than one structure in separate adjacent markers to resolve thisambiguity. However, having a plurality of markers incorporatingdifferent structures has disadvantages that the area of the substrateused for measurement markers and the measurement time for measuring allthe different measurement markers increase proportionally with a numberof structures and may increase proportionally with the decrease inambiguity.

SUMMARY

Therefore, what is needed is an effective system and method capable ofmeasuring focus and dose of an exposure apparatus while minimizing thesurface area of a mask, and thereby of a substrate, used in the process.

In an embodiment of the present invention, there is provided a method ofmeasuring focus and/or dose related properties of an exposure apparatus,the method comprising printing a marker on a substrate using theexposure apparatus to be measured and a mask including a pattern forcreating the marker, the pattern comprising an array of structures, thearray having a pitch in one direction that is resolvable by the exposureapparatus and a pitch in a second direction different from the firstdirection that is not resolvable by the exposure apparatus. The methodcontinues by measuring a property of the substrate that has been exposedby the exposure apparatus using the mask, comprising projecting aradiation beam onto the marker on the substrate and detecting radiationreflected from the marker on the substrate, and determining, from theproperties of the reflected radiation, the focus and/or dose relatedproperties of the exposure apparatus.

In another embodiment of the present invention, there is provided a maskfor use in an exposure apparatus, the mask comprising a pattern forprinting a marker on a substrate, the pattern comprising an array ofstructures, the array having a first pitch in one direction that isresolvable by the exposure apparatus and a second pitch in a seconddirection different from the first direction that is not resolvable bythe exposure apparatus.

In a further embodiment of the present invention, there is provided aprojection apparatus for use in an exposure apparatus configured toprint a marker on a substrate using a mask that contains a pattern forprinting the marker, the projection apparatus being configured toresolve the pattern on the mask in a first direction and not to resolvethe pattern in a second direction that is different from the firstdirection.

In yet another embodiment of the present invention, there is provided asubstrate comprising a marker, the marker having been printed using apattern that comprises an array of structures, the array having a pitchin one direction that is resolved in the marker and a pitch in a seconddirection different from the first direction that is not resolved in themarker.

In a still further embodiment of the present invention, there isprovided an inspection system for measuring focus and/or dose relatedproperties of an exposure apparatus, the inspection system comprising amask including a pattern for printing a marker on a substrate using theexposure apparatus to be measured, the pattern comprising an array ofstructures, the array having a pitch in one direction that is resolvableby the exposure apparatus to be measured and a pitch in a seconddirection different from the first direction that is not resolvable bythe exposure apparatus to be measured. The system also includes aninspection apparatus configured to measure a property of a substrate onwhich a marker has been printed by the exposure apparatus using themask, comprising a radiation source, a projection system configured todirect radiation from the radiation source onto the marker, a detectorconfigured to detect radiation reflected from the marker, and aprocessor configured to determine, from the properties of the reflectedradiation, the focus and/or dose related properties of the exposureapparatus.

In further embodiments of the present invention, there are provided alithographic apparatus, a lithographic cell and an inspection apparatusconfigured to measure a property of a substrate on which a marker hasbeen printed by an exposure apparatus using a mask containing a pattern,the marker having been printed using a pattern that comprises an arrayof structures, the array having a pitch in one direction that isresolved in the marker and a pitch in a second direction different fromthe first direction that is not resolved in the marker, the inspectionapparatus comprising a radiation source, a projection system configuredto direct radiation from the radiation source onto the marker, adetector configured to detect radiation reflected from the marker; and aprocessor configured to determine properties of the market comprisedfrom the detected radiation, the properties of the reflected radiation,the focus, and the dose related properties of the exposure apparatus.

Further embodiments, features, and advantages of the present invention,as well as the structure and operation of various embodiments of theinvention, are described in detail below with reference to theaccompanying drawings. It is noted that the invention is not limited tothe specific embodiments described herein. Such embodiments arepresented herein for illustrative purposes only. Additional embodimentswill be apparent to persons skilled in the relevant art(s) based on theteachings contained herein.

BRIEF DESCRIPTION OF THE DRAWINGS/FIGURES

Embodiments of the invention will now be described, by way of exampleonly, with reference to the accompanying drawings in which correspondingreference symbols indicate corresponding parts. Further, theaccompanying drawings, which are incorporated herein and form part ofthe specification, illustrate the present invention and, together withthe description, further serve to explain the principles of theinvention and to enable a person skilled in the relevant art(s) to makeand use the invention.

FIG. 1 depicts a lithographic apparatus according to an embodiment ofthe invention;

FIG. 2 depicts a lithographic cell or cluster according to an embodimentof the invention;

FIG. 3 depicts a first scatterometer according to an embodiment of theinvention;

FIG. 4 depicts a second scatterometer according to an embodiment of theinvention;

FIG. 5 depicts a focus and dose measurement pattern according to thestate of the art according to an embodiment of the invention;

FIGS. 6A and 6B depict focus and dose measurement patterns according toan embodiment of the present invention;

FIG. 7 depicts a focus and dose measurement pattern according to anembodiment of the invention;

FIG. 8 depicts a focus and dose measurement pattern according to anembodiment of the invention;

FIG. 9 depicts the relationship between focus and dose for the patternof FIG. 8, according to an embodiment of the invention;

FIG. 10A depicts the behavior of focus measurement according to thestate of the art according to an embodiment of the invention;

FIG. 10B depicts dose measurement according to the state of the artaccording to an embodiment of the invention;

FIG. 11 depicts difficulties of measuring focus and dose according to anembodiment of the invention;

FIG. 12 depicts a pattern with varying substructures according to anembodiment of the invention;

FIGS. 13A, 13B and 13C compare dose measurements using differentpatterns according to an embodiment of the invention;

FIG. 14 depicts the relationship between critical dimension, dose andfocus for different patterns according to an embodiment of theinvention;

FIGS. 15A, 15B and 15C depict relationships between sidewall angle andfocus for different patterns according to an embodiment of theinvention;

FIG. 16 depicts the relationship between sidewall angle, focus and dosefor each of the different patterns of FIG. 15, according to anembodiment of the invention; and

FIG. 17 is a table comparing dose and focus sensitivity for threedifferent patterns, according to an embodiment of the invention.

The features and advantages of the present invention will become moreapparent from the detailed description set forth below when taken inconjunction with the drawings, in which like reference charactersidentify corresponding elements throughout. In the drawings, likereference numbers generally indicate identical, functionally similar,and/or structurally similar elements. The drawing in which an elementfirst appears is indicated by the leftmost digit(s) in the correspondingreference number.

DETAILED DESCRIPTION

This specification discloses one or more embodiments that incorporatethe features of this invention. The disclosed embodiment(s) merelyexemplify the invention. The scope of the invention is not limited tothe disclosed embodiment(s). The invention is defined by the claimsappended hereto.

The embodiment(s) described, and references in the specification to “oneembodiment,” “an embodiment,” “an example embodiment,” etc., indicatethat the embodiment(s) described may include a particular feature,structure, or characteristic, but every embodiment may not necessarilyinclude the particular feature, structure, or characteristic. Moreover,such phrases are not necessarily referring to the same embodiment.Further, when a particular feature, structure, or characteristic isdescribed in connection with an embodiment, it is understood that it iswithin the knowledge of one skilled in the art to affect such feature,structure, or characteristic in connection with other embodimentswhether or not explicitly described.

Embodiments of the invention may be implemented in hardware, firmware,software, or any combination thereof. Embodiments of the invention mayalso be implemented as instructions stored on a machine-readable medium,which may be read and executed by one or more processors. Amachine-readable medium may include any mechanism for storing ortransmitting information in a form readable by a machine (e.g., acomputing device). For example, a machine-readable medium may includeread only memory (ROM); random access memory (RAM); magnetic diskstorage media; optical storage media; flash memory devices; electrical,optical, acoustical or other forms of propagated signals (e.g., carrierwaves, infrared signals, digital signals, etc.), and others. Further,firmware, software, routines, instructions may be described herein asperforming certain actions. However, it should be appreciated that suchdescriptions are merely for convenience and that such actions in factresult from computing devices, processors, controllers, or other devicesexecuting the firmware, software, routines, instructions, etc.

Before describing such embodiments in more detail, however, it isinstructive to present an example environment in which embodiments ofthe present invention may be implemented.

FIG. 1 schematically depicts a lithographic apparatus. The apparatuscomprises an illumination system (illuminator) IL configured tocondition a radiation beam B (e.g., UV radiation or DUV radiation), asupport structure (e.g., a mask table) MT constructed to support apatterning device (e.g., a mask) MA and connected to a first positionerPM configured to accurately position the patterning device in accordancewith certain parameters, a substrate table (e.g., a wafer table) WTconstructed to hold a substrate (e.g., a resist-coated wafer) W andconnected to a second positioner PW configured to accurately positionthe substrate in accordance with certain parameters, and a projectionsystem (e.g., a refractive projection lens system) PL configured toproject a pattern imparted to the radiation beam B by patterning deviceMA onto a target portion C (e.g., comprising one or more dies) of thesubstrate W.

The illumination system may include various types of optical components,such as refractive, reflective, magnetic, electromagnetic, electrostaticor other types of optical components, or any combination thereof, fordirecting, shaping, or controlling radiation.

The support structure supports, i.e., bears the weight of, thepatterning device. It holds the patterning device in a manner thatdepends on the orientation of the patterning device, the design of thelithographic apparatus, and other conditions, such as for examplewhether or not the patterning device is held in a vacuum environment.The support structure can use mechanical, vacuum, electrostatic or otherclamping techniques to hold the patterning device. The support structuremay be a frame or a table, for example, which may be fixed or movable asrequired. The support structure may ensure that the patterning device isat a desired position, for example with respect to the projectionsystem. Any use of the terms “reticle” or “mask” herein may beconsidered synonymous with the more general term “patterning device.”

The term “patterning device” used herein should be broadly interpretedas referring to any device that can be used to impart a radiation beamwith a pattern in its cross-section such as to create a pattern in atarget portion of the substrate. It should be noted that the patternimparted to the radiation beam may not exactly correspond to the desiredpattern in the target portion of the substrate, for example if thepattern includes phase-shifting features or so called assist features.Generally, the pattern imparted to the radiation beam will correspond toa particular functional layer in a device being created in the targetportion, such as an integrated circuit.

The patterning device may be transmissive or reflective. Examples ofpatterning devices include masks, programmable mirror arrays, andprogrammable LCD panels. Masks are well known in lithography, andinclude mask types such as binary, alternating phase-shift, andattenuated phase-shift, as well as various hybrid mask types. An exampleof a programmable mirror array employs a matrix arrangement of smallmirrors, each of which can be individually tilted so as to reflect anincoming radiation beam in different directions. The tilted mirrorsimpart a pattern in a radiation beam, which is reflected by the mirrormatrix.

The term “projection system” used herein should be broadly interpretedas encompassing any type of projection system, including refractive,reflective, catadioptric, magnetic, electromagnetic and electrostaticoptical systems, or any combination thereof, as appropriate for theexposure radiation being used, or for other factors such as the use ofan immersion liquid or the use of a vacuum. Any use of the term“projection lens” herein may be considered as synonymous with the moregeneral term “projection system”.

As here depicted, the apparatus is of a transmissive type (e.g.,employing a transmissive mask). Alternatively, the apparatus may be of areflective type (e.g., employing a programmable mirror array of a typeas referred to above, or employing a reflective mask).

The lithographic apparatus may be of a type having two (dual stage) ormore substrate tables (and/or two or more mask tables). In such“multiple stage” machines the additional tables may be used in parallel,or preparatory steps may be carried out on one or more tables while oneor more other tables are being used for exposure.

The lithographic apparatus may also be of a type wherein at least aportion of the substrate may be covered by a liquid having a relativelyhigh refractive index, e.g., water, so as to fill a space between theprojection system and the substrate. An immersion liquid may also beapplied to other spaces in the lithographic apparatus, for example,between the mask and the projection system. Immersion techniques arewell known in the art for increasing the numerical aperture ofprojection systems. The term “immersion” as used herein does not meanthat a structure, such as a substrate, must be submerged in liquid, butrather only means that liquid is located between the projection systemand the substrate during exposure.

Referring to FIG. 1, the illuminator IL receives a radiation beam from aradiation source SO. The source and the lithographic apparatus may beseparate entities, for example when the source is an excimer laser. Insuch cases, the source is not considered to form part of thelithographic apparatus and the radiation beam is passed from the sourceSO to the illuminator IL with the aid of a beam delivery system BDcomprising, for example, suitable directing mirrors and/or a beamexpander. In other cases the source may be an integral part of thelithographic apparatus, for example when the source is a mercury lamp.The source SO and the illuminator IL, together with the beam deliverysystem BD if required, may be referred to as a radiation system.

The illuminator IL may comprise an adjuster AD for adjusting the angularintensity distribution of the radiation beam. Generally, at least theouter and/or inner radial extent (commonly referred to as σ-outer andσ-inner, respectively) of the intensity distribution in a pupil plane ofthe illuminator can be adjusted. In addition, the illuminator IL maycomprise various other components, such as an integrator IN and acondenser CO. The illuminator may be used to condition the radiationbeam, to have a desired uniformity and intensity distribution in itscross-section.

The radiation beam B is incident on the patterning device (e.g., maskMA), which is held on the support structure (e.g., mask table MT), andis patterned by the patterning device. Having traversed the mask MA, theradiation beam B passes through the projection system PL, which focusesthe beam onto a target portion C of the substrate W. With the aid of thesecond positioner PW and position sensor IF (e.g., an interferometricdevice, linear encoder, 2-D encoder or capacitive sensor), the substratetable WT can be moved accurately, e.g., so as to position differenttarget portions C in the path of the radiation beam B. Similarly, thefirst positioner PM and another position sensor (which is not explicitlydepicted in FIG. 1) can be used to accurately position the mask MA withrespect to the path of the radiation beam B, e.g., after mechanicalretrieval from a mask library, or during a scan. In general, movement ofthe mask table MT may be realized with the aid of a long-stroke module(coarse positioning) and a short-stroke module (fine positioning), whichform part of the first positioner PM. Similarly, movement of thesubstrate table WT may be realized using a long-stroke module and ashort-stroke module, which form part of the second positioner PW. In thecase of a stepper (as opposed to a scanner) the mask table MT may beconnected to a short-stroke actuator only, or may be fixed. Mask MA andsubstrate W may be aligned using mask alignment marks M1, M2 andsubstrate alignment marks P1, P2. Although the substrate alignment marksas illustrated occupy dedicated target portions, they may be located inspaces between target portions (these are known as scribe-lane alignmentmarks). Similarly, in situations in which more than one die is providedon the mask MA, the mask alignment marks may be located between thedies.

The depicted apparatus could be used in at least one of the followingmodes:

1. In step mode, the mask table MT and the substrate table WT are keptessentially stationary, while an entire pattern imparted to theradiation beam is projected onto a target portion C at one time (i.e., asingle static exposure). The substrate table WT is then shifted in the Xand/or Y direction so that a different target portion C can be exposed.In step mode, the maximum size of the exposure field limits the size ofthe target portion C imaged in a single static exposure.

2. In scan mode, the mask table MT and the substrate table WT arescanned synchronously while a pattern imparted to the radiation beam isprojected onto a target portion C (i.e., a single dynamic exposure). Thevelocity and direction of the substrate table WT relative to the masktable MT may be determined by the (de-) magnification and image reversalcharacteristics of the projection system PL. In scan mode, the maximumsize of the exposure field limits the width (in the non-scanningdirection) of the target portion in a single dynamic exposure, whereasthe length of the scanning motion determines the height (in the scanningdirection) of the target portion.

3. In another mode, the mask table MT is kept essentially stationaryholding a programmable patterning device, and the substrate table WT ismoved or scanned while a pattern imparted to the radiation beam isprojected onto a target portion C. In this mode, generally a pulsedradiation source is employed and the programmable patterning device isupdated as required after each movement of the substrate table WT or inbetween successive radiation pulses during a scan. This mode ofoperation can be readily applied to maskless lithography that utilizesprogrammable patterning device, such as a programmable mirror array of atype as referred to above.

Combinations and/or variations on the above described modes of use orentirely different modes of use may also be employed.

As shown in FIG. 2, the lithographic apparatus LA forms part of alithographic cell LC, also sometimes referred to a lithocell or cluster,which also includes apparatus to perform pre- and post-exposureprocesses on a substrate. Conventionally these include spin coaters SCto deposit resist layers, developers DE to develop exposed resist, chillplates CH and bake plates BK. A substrate handler, or robot, RO picks upsubstrates from input/output ports I/O1, I/O2, moves them between thedifferent process apparatus and delivers then to the loading bay LB ofthe lithographic apparatus. These devices, which are often collectivelyreferred to as the track, are under the control of a track control unitTCU which is itself controlled by the supervisory control system SCS,which also controls the lithographic apparatus via lithography controlunit LACU. Thus, the different apparatus can be operated to maximizethroughput and processing efficiency.

In order that the substrates that are exposed by the lithographicapparatus are exposed correctly and consistently, it is desirable toinspect exposed substrates to measure properties such as overlay errorsbetween subsequent layers, line thicknesses, critical dimensions (CD),etc. If errors are detected, adjustments may be made to exposures ofsubsequent substrates, especially if the inspection can be done soon andfast enough that other substrates of the same batch are still to beexposed. Also, already exposed substrates may be stripped and reworked,e.g., to improve yield, or discarded, thereby avoiding performingexposures on substrates that are known to be faulty. In a case whereonly some target portions of a substrate are faulty, further exposurescan be performed only on those target portions which are good.

An inspection apparatus is used to determine the properties of thesubstrates, and in particular, how the properties of differentsubstrates or different layers of the same substrate vary from layer tolayer. The inspection apparatus may be integrated into the lithographicapparatus LA or the lithocell LC or may be a stand-alone device. Toenable most rapid measurements, it is desirable that the inspectionapparatus measure properties in the exposed resist layer immediatelyafter the exposure. However, the latent image in the resist has a verylow contrast, such that there is only a very small difference inrefractive index between the parts of the resist which have been exposedto radiation and those which have not, and not all inspection apparatushave sufficient sensitivity to make useful measurements of the latentimage. Therefore measurements may be taken after the post-exposure bakestep (PEB) which is customarily the first step carried out on exposedsubstrates and increases the contrast between exposed and unexposedparts of the resist. At this stage, the image in the resist may bereferred to as semi-latent. It is also possible to make measurements ofthe developed resist image, at which point either the exposed orunexposed parts of the resist have been removed, or after a patterntransfer step such as etching. The latter possibility limits thepossibilities for rework of faulty substrates but may still provideuseful information.

FIG. 3 depicts a scatterometer which may be used in an embodiment of thepresent invention. It comprises a broadband (white light) radiationprojector 2 which projects radiation onto a substrate W. The reflectedradiation is passed to a spectrometer detector 4, which measures aspectrum 10 (intensity as a function of wavelength) of the specularreflected radiation. From this data, the structure or profile givingrise to the detected spectrum may be reconstructed by processing unitPU, e.g., by Rigorous Coupled Wave Analysis and non-linear regression orby comparison with a library of simulated spectra as shown at the bottomof FIG. 3. In general, for the reconstruction the general form of thestructure is known and some parameters are assumed from knowledge of theprocess by which the structure was made, leaving only a few parametersof the structure to be determined from the scatterometry data. Such ascatterometer may be configured as a normal-incidence scatterometer oran oblique-incidence scatterometer.

Another scatterometer that may be used with the present invention isshown in FIG. 4. In this device, the radiation emitted by radiationsource 2 is focused using lens system 12 through interference filter 13and polarizer 17, reflected by partially reflected surface 16 and isfocused onto substrate W via a microscope objective lens 15, which has ahigh numerical aperture (NA), for example, preferably at least about0.9, and more preferably at least about 0.95. Immersion scatterometersmay even have lenses with numerical apertures over 1. The reflectedradiation then transmits through partially reflective surface 16 into adetector 18 in order to have the scatter spectrum detected. The detectormay be located in the back-projected pupil plane 11, which is at thefocal length of the lens system 15, however the pupil plane may insteadbe re-imaged with auxiliary optics (not shown) onto the detector. Thepupil plane is the plane in which the radial position of radiationdefines the angle of incidence and the angular position defines azimuthangle of the radiation. In one example, the detector is atwo-dimensional detector so that a two-dimensional angular scatterspectrum of a substrate target 30 can be measured. The detector 18 maybe, for example, an array of CCD or CMOS sensors, and may use anintegration time of, for example, 40 milliseconds per frame.

A reference beam is often used for example to measure the intensity ofthe incident radiation. To do this, when the radiation beam is incidenton the beam splitter 16 part of it is transmitted through the beamsplitter as a reference beam towards a reference mirror 14. Thereference beam is then projected onto a different part of the samedetector 18.

A set of interference filters 13 is available to select a wavelength ofinterest in the range of, say, 405-790 nm or even lower, such as 200-300nm. The interference filter may be tunable rather than comprising a setof different filters. A grating could be used instead of interferencefilters.

The detector 18 may measure the intensity of scattered light at a singlewavelength, or narrow wavelength range, the intensity separately atmultiple wavelengths or integrated over a wavelength range. Furthermore,the detector may separately measure the intensity of transverse magneticand transverse electric polarized light and/or the phase differencebetween the transverse magnetic and transverse electric polarized light.

Using a broadband light source (i.e., one with a wide range of lightfrequencies or wavelengths, and therefore of colors) is possible, whichgives a large etendue, allowing the mixing of multiple wavelengths. Theplurality of wavelengths in the broadband each has a bandwidth of λ8 anda spacing of at least 2λ8 (i.e., twice the bandwidth). A plurality of“sources” of radiation may be different portions of an extendedradiation source which have been split using fiber bundles. In this way,angle resolved scatter spectra can be measured at multiple wavelengthsin parallel. A 3-D spectrum, for example, such as wavelength and twodifferent angles, can be measured, which contains more information thana 2-D spectrum. This allows more information to be measured whichincreases metrology process robustness. This is described in more detailin European Patent No. 1,628,164A, which is incorporated by referenceherein in its entirety.

The target 30 on substrate W may be a grating, which is printed suchthat after development, the bars are formed of solid resist lines. Thebars may alternatively be etched into the substrate. This pattern issensitive to chromatic aberrations in the lithographic projectionapparatus, particularly the projection system PL, and illuminationsymmetry and the presence of such aberrations will manifest themselvesin a variation in the printed grating. Accordingly, the scatterometrydata of the printed gratings is used to reconstruct the gratings. Theparameters of the grating, such as line widths and shapes, may be inputto the reconstruction process, performed by processing unit PU, fromknowledge of the printing step and/or other scatterometry processes.

The present invention relates to embodiments of a pattern for use on amask in an exposure apparatus. The mask of the exposure apparatus may bea transmissive mask, or it may be a reflective mask such as a pluralityof individually controllable elements such as mirrors. This mask is usedby the exposure apparatus, for example, such as in a lithographicapparatus, to print a marker on a substrate. The marker, or printedpattern, on the substrate is then measured using an inspection apparatussuch as a scatterometer or an ellipsometer. Any sort of inspectionapparatus may be used as long as it is an inspection apparatus that iscapable of measuring radiation that is reflected from a printedstructure such as a grating and that may measure parameters of thepattern such as critical dimension (CD) of individual structures withinthe printed pattern; or sidewall angle (SWA) of the same structures.

The properties of the reflected radiation or the measurements of themarker on the substrate are compared with mathematical models orlibraries of previous measurements or simulations and extrapolations ofthe relationship between these properties (of the reflected radiation orCD or SWA) and focus and/or dose related properties of the exposureapparatus used to print the marker. The focus and/or dose relatedproperties may be focus offset (which may be caused by misalignment oflenses, for instance) or dose offset (caused by fluctuations in theintensity of the radiation beam, for instance). They may also be otherfocus related parameters like astigmatism, contrast or lens aberrations(typically expressed in zernikes). Alternatively, they may beillumination (i.e., radiation) parameters such as dose or intensityvariation. Yet alternatively, the measured properties may be parametersthat have an impact on the resist that is similar to the impact causedby dose, such as local bakeplate temperature (which gives rise tosimilar variations over a substrate surface in reflected radiation or CDor SWA as variations in dose over the substrate surface do) and resistvariation (again, variation in resist thickness or density, etc., willgive rise to variations in CD and SWA, etc., in a similar way tovariations in dose).

An example of a situation in which only offsets in dose (and notnecessarily focus) can be measured is as follows. A substrate, once ithas been exposed, may be put on a bakeplate, which is a heated platethat dries the resist layer that is on the substrate in order to fix thepattern that has been exposed on it. The heat of the bakeplate on thebottom surface of the substrate has similar properties to intensity ofradiation on the top surface of the substrate. If the temperature of thebakeplate is not homogeneous, the resist will not dry uniformly.Measurement of features on the resist (e.g., in a plurality of markerson the substrate) may be measured using the system described above inthe same way as measurements are made of dose. Any variations in “dose”that are determined may in fact be variations in temperature of thebakeplate and the bakeplate may be adjusted accordingly to correct forthe variations. Indeed, the same markers in the pattern fields of asubstrate may be used first to measure dose variations that exist in theexposure tool, and then variations that exist in the bakeplate, takingthe dose variations in the exposure tool into consideration for thelater measurements. The markers in this case need only be dosesensitive.

FIG. 5 shows a grating G that includes an array in one dimension of barsB (note that it is the array that is in one dimension, rather than thatthe bars are one-dimensional). This is an example of a pattern that iscommonly used in measuring characteristics such as overlay and alignmentof substrates W in lithographic apparatuses. However, as mentionedabove, when radiation is reflected from this grating G and parameterssuch as critical dimension and sidewall angle are determined from thereflected radiation, there can be several combinations of focus and dosethat will give rise to the CD and SWA measurements that have been made.

One embodiment of the present invention comprises the creation of apattern 30 such as that shown in FIG. 6A. The pattern 30 is now atwo-dimensional array of structures 40. A feature of the presentembodiment is that the two-dimensional repeating structures 40 havedifferent physical or geometric properties in each of the x and ydirections. Because of the different physical or geometric properties ineach of the x and y directions, each of the orientations has asignificant and intentionally different response to focus and dosevariations. This results in a more complex overall behavior of theprinted structure than mere critical dimension and sidewall angle. As aresult, the overall response is unique for a given focus and dose, whichenables better separation of focus and dose when compared withmeasurements of a single one-dimensional array. Combinations ofdifferent properties in a single repeating structure according to anembodiment of the invention enables a single marker to be used and meansthat measurements can be made on a single marker, thus reducing spaceused on the mask for the pattern, for example, when compared with usinga plurality of markers each containing a one-dimensional array or asingle structure, and space used on the substrate for the exposedmarker, as well as reducing time taken to take the measurements whileincreasing the reduction in ambiguity of the measurement results.

FIG. 6B shows an alternative form of pattern, which may be referred toas a Zebra pattern because of its striped configuration. As can be seenin FIG. 6B, the Zebra pattern has a coarse pitch P in a first directionand a fine pitch p in the orthogonal direction. The coarse pitch P ispart of the duty cycle of the Zebra striped pattern, which is varied foroptimization based on the focus/dose sensitivity of various illuminationmodes, i.e., depending on the polarization, wavelength, intensity, etc.,of the radiation beam used to irradiate the pattern on the mask toproduce the desired testing marker on the substrate. The coarse pitchmay be varied between about 400 to about 600 nm, for instance.

Additionally, or alternately, the fine pitch p is not varied because canbe fixed at a size smaller than can be printed by the exposureapparatus. For example, the fine pitch may be fixed at approximately 70nm. The reason that a small pitch is not printed onto the substrate bythe exposure apparatus is linked to the wavelength of the exposureradiation used. In the present example, the fine pitch is approximately70 nm because the resolution of a known lithographic apparatus is about80 nm, and the fine pitch can be sub-resolution. However, a lithographicapparatus that uses EUV radiation is envisaged by the embodiments ofpresent invention, which has a much smaller resolution such that thefine pitch may be about 50 nm, 30 nm or even 10 nm.

The structures that are not printed onto the substrate (e.g., becausethey are not resolvable by the exposure apparatus) nevertheless affectthe way in which other structures that are printable are printed, in asimilar way to the way assist features work. However, the presentpatterns are designed to respond particularly to focus and dose.

FIG. 6B also shows a coarse critical dimension CD in the same directionas the coarse pitch P, and fine critical dimension CD in the orthogonaldirection. Either of these measurements is variable according toillumination modes. The coarse critical dimension CD may be variedbetween about 200 and 300 nm, for instance, and the fine criticaldimension cd may be of the order of about 30-40 nm, with the pitchmeasurements given above.

In the examples given above for FIG. 6B, the total Zebra pattern may beof the order of about 40 by 40 μm.

The pattern is designed to be of high sensitivity to focus and dose andto be in a small process window. The product area, on the other hand,within the same mask and therefore on the same field of the substratethat is printed using the same mask, is at as low a dose and focussensitivity as possible and incorporates a large process window. In thisway, the product and test patterns do not affect each other, and theproduct has the more important area on the mask as on the substrate.

As an alternative to the bar-and-space grating layout of the Zebrapattern, the two-dimensional pattern may be made up of other structuressuch as contact holes or any other shape that allows one pitch directionto be unprintable by the exposure apparatus.

Several different pattern structures are possible and will be imaginedby this person skilled in the art. Many alternative segmentations may beused, such as segmenting lines and/or spaces in either or both of the xand y directions, or even incorporating exotic structures likenanocombs. More examples are described below.

Alternatively, a one-dimensional repeating structure may be used as apattern, starting with a base as shown in FIG. 7. This one-dimensionalpattern is effectively the same as the Zebra pattern of FIG. 6B, but thefine pitch p disappears completely to give solid bars 50 as shown inFIG. 7. A pattern 30 with a unit cell or single structure 40 is dividedinto substructures 50. In one example, there are preferably severalsubstructures per unit cell 40 such that the response of the differentsubstructures of the unit cell to focus and dose may be individually andseparately measured. The pattern of FIG. 7 is repeated several times,and represents a unit cell containing substructures that are differentin the x and y directions. The bars of FIG. 7 may be divided intodifferent subsegments as shown in, for example, FIG. 12, which isdescribed later.

FIG. 8 shows an alternative pattern 30 with structures 40 that aredifferent in the x and y directions. The response of these structuredimensions to focus and dose variations is shown in FIG. 9. In thisexample, the line width in the y direction is mainly dependent on dose.In the x direction, the line width is mainly dependent on focus. Thevarious images 45 shown in FIG. 9 are the resulting printed structureson the substrate after exposure, as a function of focus and dose.

In order to determine focus and dose from critical dimension or sidewallangle, a focus dose model is created. The critical dimensions (CD) andsidewall angles (SWA) of a focus energy matrix (FEM) are measured tocover a large range of focus and dose values. From this, a mathematicalmodel is created that describes and interpolates the relationshipbetween focus and dose and CD and SWA. With this interpolated model, anysingle CD and/or SWA measurement can be converted to focus and dose.

A good focus/dose model should be able to predict the focus and dosevalues for the same measurement target structures that were used to setup the model in the first place. This is tested in a “self test”, whereset point values and focus and dose are plotted against the predictedvalues of the target structures as shown in FIGS. 10A and 10B. Ideally,a straight line with a slope 1 is obtained. In other words, the measuredmodel values should be the same as the predicted values. For someone-dimensional structures, however, the focus dose model is unable todetermine the correct focus value because of the fact that not enoughdifferences are observed between the printed structure exposed atnegative focus values and at positive focus values as shown in FIG. 10A.Negative focus values are where the focal point of the radiation is toone side of the substrate surface; and positive focus values are wherethe focal point is on the other side of the same substrate surface. Zerowould be the substrate surface where focus of the radiation is desired.FIG. 10A shows set focus positions along the bottom axis and predictedvalues along the vertical axis. As can be seen, the predicted values arealmost all positive, which is a problem with classical one-dimensionalstructures. Dose determination fares slightly better as shown in FIG.10B, where a straight line with a slope of 1 is possible between setdose and predicted dose.

Other issues with non-uniqueness of pattern structure properties resultin a large scattering in predicted focus and dose values. This is shownin FIG. 11. Depending on the structures, the location in the focus anddose prediction graphs determine how accurate focus and dose can bedetermined. Noise estimates show that for certain regions in the graph,focus and dose are more difficult to determine, as shown by the largescattering in graphs C and D corresponding to noisy areas of focusagainst dose measurement results. In a reproducibility test, the samemarker is measured multiple times, after which the focus and dose valuesare determined. In FIG. 11, it is shown that for the circled area ofnoise plots that are in the center of the Figure, the lower right handcorner circled area gives rise to higher scattering than for the centercircled area of the noise plots.

The advantage of focus and/or dose determination withtwo-dimensional-repeating structures or one-dimensional-repeatingstructures with more than one substructure in each unit cell is that thepatterns can be designed to be more robust for separating focus and doseinformation from a single structure in a wider range of radiationconditions and resist and stack properties. This improves the focus-dosemeasurement potential for resists and for more complex underlyingtopography. Apart from focus and dose, the additional information frommore than two varying properties (i.e., CD and SWA) of the structure canbe used to resolve other process or exposure parameters of interest.

An example of a pattern that contains substructures in alternate linesis shown in FIG. 12. This pattern (which can be present on a mask, forinstance, for printing onto the substrate) will print as shown, so thatthe resultant marker on the substrate will appear the same as the mask'sprinting pattern. In the x-direction, the marker is dose-sensitive, butnot focus-sensitive. This is because the marker generally acts as aregular dense target in the x-direction, which means that variation infocus does not affect it. However, in the y-direction, the marker isboth dose- and focus-sensitive because of the larger gap. By usingnon-conventional (e.g., annular) radiation beam shapes, radiationdiffracted because of the marker in the y-direction (during theinspection phase) can be discerned from the diffraction in thex-direction. By filtering appropriately in the pupil plane, focus anddose can thereby be discriminated from each other, for example, byinvestigating CD measurements of the normal lines and the chopped linesof the marker shown in FIG. 12.

One of the keys of using sub-arrays or substructures within arrays isthat this changes the transmissivity of the pattern (or marker) in atleast one direction. The reason for this is that the CD of structures iswhat affects the transmissivity to radiation of the pattern. The CD ofthe structures may be varied to affect the transmissivity of thepattern, depending on what properties of the exposure apparatus arebeing measured.

As long as a structure that can be measured as a line is printed ontothe substrate, focus measurements can be made. When there is a change intransmissivity, dose properties can be measured. Another example of apattern that can be used to measure dose and focus (or other relatedproperties) is a checkerboard pattern, with the dark squares (or othershape) being structures (including holes or dots), and the light squares(or other shape) being spaces between the structures. The relative sizesof the structures and spaces may be altered to affect transmissivity, orthe structures may vary in size and/or shape from one 1-D or 2-D arrayto the next. Alternatively, to measure dose and focus/dose, thestructures and spaces may be arranged to be printable in one directionbut not in the other, as described in relation to FIG. 12 above.

From any such periodic 2-D pattern, both focus and dose may bedetermined from any of the following methods, which are not meant tolimit the scope of the invention nor be an exhaustive list:

1. focus and dose being measured directly from a diffraction spectrum ofradiation reflected from the pattern (e.g., by comparing with expected,modeled or simulated diffraction spectra);

2. focus and dose being measured using an overlay measurement, where amarker printed from a pattern such as that described above is printed onconsecutive layers on a substrate and the overlay offset of theconsecutive layers is measured by investigating the behavior ofradiation reflected from the superimposed layers compared with expectedbehavior;

3. focus and dose being measured using the reconstruction of SWA, CD andother physical properties of structures on the substrate using variousdirect and indirect measurement techniques; and

4. focus and dose being measured by investigating radiation informationat the pupil plane (where diffracted radiation is effectively focusedand can be investigated).

The resultant focus and dose related measurements are fed back or fedforward to the exposure apparatus, which then compensates for any errorin either measurement.

FIGS. 13 through 17 depict the comparison of simulations that have beencarried out comparing standard one-dimensional patterns with standardone-dimensional patterns that include assist features and withtwo-dimensional patterns as described above. In the specific examplesshown, the pitch of all of the patterns was about 380 nm, except for thetwo-dimensional pattern shown in FIGS. 13C and 15C, which have a(coarse) pitch in the x direction of about 380 nm but a (fine) pitch inthe y direction of about 150 nm. In all of the examples, the resistthickness was about 125 nm.

FIG. 13A shows a pattern with a single structure in the shape of a bar.A comparison of measured critical dimension (shown as mean criticaldirection MCD in the figures) is compared with dose. As can be seen fromthe graph of FIG. 13A, the slopes are not very steep, which means thatthe sensitivity of CD to dose is low. Each of the lines in the graphrelates to different focus values (in μm).

FIG. 13B depicts a pattern with assist features. By assist features, itis meant that further structures are included in the pattern on the maskin order to compensate for edge of structure errors and blurring thatcan appear on printed patterns. The structures 55 are the assistfeatures to the main structure 40 as shown in FIG. 13B. Although theseassist features 55 appear on the mask pattern, they do not appear in theprinted structure on a substrate because they are too small to bedistinguished by the wavelength used and/or fully compensated for incanceling out any edge errors of the main structure 40. As can be seenon the graph in FIG. 13B, the assist features cause the slope of the CDagainst dose to be steeper than without the assist features.

FIG. 13C shows a pattern 30 with two-dimensional periodic structures 40according to an embodiment of the present invention. As can be seen fromthe graph, for any fixed value of focus, the slope of CD against dose issteeper on average even than the graph for the pattern with the assistfeatures. This means that the (CD of the) 2D pattern is more sensitiveto dose than other patterns tested.

FIG. 14 compares the slopes of each of the patterns of FIG. 13 with afocus value. The larger the overall absolute values of the slopes (orthe more negative these values), the more sensitive the pattern, whichcan be described alternatively as the less space under the graph, themore sensitive the pattern used. The two-dimensional target achievesthis more than the pattern either with or without assist features.

FIG. 15 illustrate the same measurements as FIG. 13, but for sidewallangle compared with focus measurements. As with FIG. 13, FIG. 15Adepicts a mask pattern with a single structure 40. The graph of SWAagainst focus is also shown in the same figure. FIG. 15B shows a graphof SWA against focus for a pattern with a main structure 40 and assistfeatures 55. Finally, FIG. 15C shows a graph for SWA against focus for atwo-dimensional pattern 30 with structures 40 that are different in thex and y directions. The two-dimensional pattern results in a steeperaverage slope of SWA against focus than either of the other twopatterns. FIG. 16 shows the slope from the graphs of FIGS. 15A, 15B and15C against measured dose. The graph of FIG. 16 shows that the slopeagainst dose is steeper for the two-dimensional pattern than for theother two patterns.

FIG. 17 shows a table of dose sensitivity and focus sensitivity for eachof the three patterns shown in FIGS. 13 and 15. As can be seen from thetable, dose and focus sensitivity increases from the pattern with noassist features to the pattern with assist features and again to thepattern with a two-dimensional structure array. These results are for adose between 12.5 and 13.5 mJ/cm2 and focus of −0.100 to −0.050 μm.

The two-dimensional patterns therefore have been shown in tests to bemore sensitive to dose and focus than other types of known patterns.

Although specific reference may be made in this text to the use oflithographic apparatus in the manufacture of ICs, it should beunderstood that the lithographic apparatus described herein may haveother applications, such as the manufacture of integrated opticalsystems, guidance and detection patterns for magnetic domain memories,flat-panel displays, liquid-crystal displays (LCDs), thin film magneticheads, etc. The skilled artisan will appreciate that, in the context ofsuch alternative applications, any use of the terms “wafer” or “die”herein may be considered as synonymous with the more general terms“substrate” or “target portion”, respectively. The substrate referred toherein may be processed, before or after exposure, in for example atrack (a tool that typically applies a layer of resist to a substrateand develops the exposed resist), a metrology tool and/or an inspectiontool. Where applicable, the disclosure herein may be applied to such andother substrate processing tools. Further, the substrate may beprocessed more than once, for example in order to create a multi-layerIC, so that the term substrate used herein may also refer to a substratethat already contains multiple processed layers.

Although specific reference may have been made above to the use ofembodiments of the invention in the context of optical lithography, itwill be appreciated that the invention may be used in otherapplications, for example imprint lithography, and where the contextallows, is not limited to optical lithography. In imprint lithography atopography in a patterning device defines the pattern created on asubstrate. The topography of the patterning device may be pressed into alayer of resist supplied to the substrate whereupon the resist is curedby applying electromagnetic radiation, heat, pressure or a combinationthereof. The patterning device is moved out of the resist leaving apattern in it after the resist is cured.

The terms “radiation” and “beam” used herein encompass all types ofelectromagnetic radiation, including ultraviolet (UV) radiation (e.g.,having a wavelength of or about 365, 355, 248, 193, 157 or 126 nm) andextreme ultra-violet (EUV) radiation (e.g., having a wavelength in therange of 5-20 nm), as well as particle beams, such as ion beams orelectron beams.

The term “lens”, where the context allows, may refer to any one orcombination of various types of optical components, includingrefractive, reflective, magnetic, electromagnetic and electrostaticoptical components.

While specific embodiments of the invention have been described above,it will be appreciated that the invention may be practiced otherwisethan as described. For example, the invention may take the form of acomputer program containing one or more sequences of machine-readableinstructions describing a method as disclosed above, or a data storagemedium (e.g., semiconductor memory, magnetic or optical disk) havingsuch a computer program stored therein.

CONCLUSION

It is to be appreciated that the Detailed Description section, and notthe Summary and Abstract sections, is intended to be used to interpretthe claims. The Summary and Abstract sections may set forth one or morebut not all exemplary embodiments of the present invention ascontemplated by the inventor(s), and thus, are not intended to limit thepresent invention and the appended claims in any way.

The present invention has been described above with the aid offunctional storing blocks illustrating the implementation of specifiedfunctions and relationships thereof. The boundaries of these functionalstoring blocks have been arbitrarily defined herein for the convenienceof the description. Alternate boundaries can be defined so long as thespecified functions and relationships thereof are appropriatelyperformed.

The foregoing description of the specific embodiments will so fullyreveal the general nature of the invention that others can, by applyingknowledge within the skill of the art, readily modify and/or adapt forvarious applications such specific embodiments, without undueexperimentation, without departing from the general concept of thepresent invention. Therefore, such adaptations and modifications areintended to be within the meaning and range of equivalents of thedisclosed embodiments, based on the teaching and guidance presentedherein. It is to be understood that the phraseology or terminologyherein is for the purpose of description and not of limitation, suchthat the terminology or phraseology of the present specification is tobe interpreted by the skilled artisan in light of the teachings andguidance.

The breadth and scope of the present invention should not be limited byany of the above-described exemplary embodiments, but should be definedonly in accordance with the following claims and their equivalents.

1. A method comprising: printing a marker on a substrate using anexposure apparatus and a mask, the mask including a pattern for creatingthe marker, the pattern comprising a two-dimensional array of structuresarranged such that the marker includes repeating structures having adifferent response to a focus and a dose of the exposure apparatus ineach of an x direction and a y direction; and measuring a property ofthe substrate that has been exposed by the exposure apparatus and themask, the measuring comprising: projecting a radiation beam onto themarker on the substrate; detecting radiation reflected from the markeron the substrate; and determining, from the properties of the reflectedradiation, at least one of the focus and the dose of the exposureapparatus.
 2. The method according to claim 1, wherein a result of atleast one of the focus and the dose related measurements of the exposureapparatus being measured is fed back to the exposure apparatus forcorrection of any errors in at least one of the focus and the doserelated properties.
 3. The method according to claim 1, furthercomprising: printing the marker on the substrate using at least one offocus and dose offsets; measuring a variation of properties of thereflected radiation as a function of the at least one of focus and doseoffsets; and storing a library of relationships between properties ofthe reflected radiation and at least one of focus and dose offsets basedon the measurement of the variation of the properties.
 4. The methodaccording to claim 1, further comprising: simulating at least one of themarker pattern and the reflected radiation in response to variousoffsets of at least one of focus and dose of the exposure apparatus; andstoring a mathematical model of the at least one of the marker patternand the reflected radiation characteristics for various focus at leastone of focus and dose offsets based on the simulations.
 5. The method ofclaim 1, wherein a line width of the repeating structures of the markerin the x direction is dependent more on focus than on dose.
 6. Themethod of claim 1, wherein a line width of the repeating structures ofthe marker in the y direction is dependent more on dose than on focus.7. A mask comprising: a pattern arranged for printing a marker on asubstrate using an exposure apparatus, the pattern comprising atwo-dimensional array of structures, wherein the structures are arrangedsuch that the marker includes repeating structures having a differentresponse to a focus and a dose of the exposure apparatus in each of an xdirection and a y direction.
 8. The mask of claim 7, wherein a linewidth of the repeating structures of the marker in the x direction isdependent more on focus than on dose.
 9. The mask of claim 7, wherein aline width of the repeating structures of the marker in the y directionis dependent more on dose than on focus.
 10. An inspection apparatusconfigured to measure a property of a substrate on which a marker hasbeen printed by an exposure apparatus using a mask containing a patterncomprising a two-dimensional array of structures arranged such that themarker includes repeating structures having a different response to afocus and a dose of the exposure apparatus in each of an x direction anda y direction, the inspection apparatus comprising: a radiation source;a projection system configured to direct radiation from the radiationsource onto the marker; a detector configured to detect radiationreflected from the marker; and a processor configured to determineproperties of the reflected radiation and, from the properties of thereflected radiation, determine at least one of focus and dose relatedproperties of the exposure apparatus used to print the marker.
 11. Theinspection apparatus according to claim 10, wherein the processor isconfigured to determine the at least one of focus and dose relatedproperties of the exposure apparatus by comparing the reflectedradiation with a library of at least one of previously measured,simulated and extrapolated relationships between properties of thereflected radiation and the at least one of focus and dose relatedproperties.
 12. The inspection apparatus according to claim 10, whereina line width of the repeating structures of the marker in the xdirection is dependent more on focus than on dose.
 13. The inspectionapparatus according to claim 10, wherein a line width of the repeatingstructures of the marker in the y direction is dependent more on dosethan on focus.
 14. A lithographic cell comprising: a coater arranged tocoat a substrate with a radiation sensitive layer; an exposure apparatusconfigured to expose an image onto the radiation sensitive layer of thesubstrate coated by the coater; a developer configured to develop theimage exposed by the exposure apparatus; and an inspection apparatusconfigured to measure a property of a substrate on which a marker hasbeen printed by the exposure apparatus using a mask containing apattern, the pattern comprising a two-dimensional array of structuresarranged such that the marker includes repeating structures having adifferent response to a focus and a dose of the exposure apparatus ineach of an x direction and a y direction, the inspection apparatuscomprising, a radiation source, a projection system configured to directradiation from the radiation source onto the marker, a detectorconfigured to detect radiation reflected from the marker, and aprocessor configured to determine properties of the reflected radiationand, from the properties of the reflected radiation, determine at leastone of focus and dose related properties of the exposure apparatus usedto print the marker.
 15. The lithographic cell according to claim 14,wherein the processor is configured to determine the at least one offocus and dose related properties of the exposure apparatus by comparingthe reflected radiation with a library of at least one of previouslymeasured, simulated and extrapolated relationships between properties ofthe reflected radiation and the at least one of focus and dose relatedproperties.
 16. The lithographic cell according to claim 14, wherein aline width of the repeating structures of the marker in the x directionis dependent more on focus than on dose.
 17. The lithographic cellaccording to claim 14, wherein a line width of the repeating structuresof the marker in the y direction is dependent more on dose than onfocus.